@TechReport{ it:2011-008,
author = {Kenneth Duru and Ken Mattsson and Gunilla Kreiss},
title = {Stable and Conservative Time Propagators for Second Order
Hyperbolic Systems},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2011},
number = {2011-008},
month = apr,
abstract = {In this paper we construct a hierarchy of arbitrary high
(even) order accurate explicit time propagators for
semi-discrete second order hyperbolic systems. An accurate
semi-discrete problem is obtained by approximating the
corresponding spatial derivatives using high order accurate
finite difference operators satisfying the summation by
parts rule. In order to obtain a strictly stable
semi-discrete problem, boundary conditions are imposed
weakly using the simultaneous approximation term method.
The time discretization starts with a second order central
difference scheme, then using the modified equation
approach (even in the presence of a first order derivative
in time) we derive arbitrary high order accurate time
marching schemes. For the fully discrete problem, we
introduce a suitable weighted inner product and use the
energy method to derive an optimal CFL condition, which
provides a useful and rigorous criterion for stability.
Numerical examples are also provided. }
}